Equilibrium constant heterogeneous reactions

Conditional equilibrium constants for reactions in heterogeneous chemical system.s are discu.ssed fully in Chap. 5 of G. Sposito. op, cit. ... 

Definitions. Define briefly (a) equilibrium, (b) equilibrium constant, (c) reaction quotient, (d) equilibrium condition, (e) heterogeneous equilibrium, (f) Le Chatelier principle. Choose a reaction and use it to illustrate each of these concepts. 

A quite analogous treatment may be applied to the kinetics of heterogeneously catalyzed reactions. Consider a surface S that contains so active sites to which reactant A, a gaseous or solute species, may bind reversibly with an equilibrium constant KA ... 

The equilibrium constants for heterogeneous reactions are also given by the general expression in Eq. 2 all we have to remember is that the activity of a pure solid or liquid is 1. For instance, for the calcium hydroxide equilibrium (reaction H),... 

Distinguish homogeneous and heterogeneous equilibria and write equilibrium constants for both types of reaction from a balanced equation (Example 9.1 and Self-Tests 9.2 and 9.5). 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

In all metallurgical processing, heterogeneous reactions and the approach to equilibrium between two or more phases are of great importance. Much of the information on equilibrium is contained in the equilibrium constant which, as mentioned earlier, is related to the standard free energy change by the equation... 

For a heterogeneous reaction, the state of all components is not uniform, for example, a reaction between a gas and a liquid. This requires standard states to be defined for each component. The activity of a solid in the equilibrium constant can be taken to be unity. 

The principle we have applied here is called microscopic reversibility or principle of detailed balancing. It shows that there is a link between kinetic rate constants and thermodynamic equilibrium constants. Obviously, equilibrium is not characterized by the cessation of processes at equilibrium the rates of forward and reverse microscopic processes are equal for every elementary reaction step. The microscopic reversibility (which is routinely used in homogeneous solution kinetics) applies also to heterogeneous reactions (adsorption, desorption dissolution, precipitation). 

The interpretation of slopes also requires meaningful rate data. When the reaction consists of a series of elementary steps (and this is always so with heterogeneous catalytic reactions), the rate coefficients obtained from a superficial treatment of a limited set of measurements may be composites of several rate and equilibrium constants for individual steps, in favorable cases constituting a product. As every step may be influenced by the substituents, the resulting effect can be easily attributed to a false elementary step. 

York, 1963] that there are three fundamental gasification reactions the Boudouard reaction (24-17), the heterogeneous water-gas-shift reaction (24-18), and the hydrogasification reaction (24-15). The equilibrium constants for these reactions are sufficient to calculate equi-... 

The equilibrium law for a heterogeneous reaction is written without concentration terms for pure solids or liquids since their concentration is a constant. 

For enzyme reactions K is the traditional Michaelis constant. For a heterogeneous surface on which adsorption and desorption but no reaction occurs (k2 = 0) K is simply an equilibrium constant for adsorption. (Actually we are not being as economical as we could be in this non-dimensionalization of the equations. We could have divided throughout by K instead of introducing the pressure scale p°, and eqn (12.9) would then have read... 

For each reaction in a surface chemistry mechanism, one must provide a temperature dependent reaction probability or a rate constant for the reaction in both the forward and reverse directions. (The user may specify that a reaction is irreversible or has no temperature dependence, which are special cases of the general statement above.) To simulate the heat consumption or release at a surface due to heterogeneous reactions, the (temperature-dependent) endothermicity or exothermicity of each reaction must also be provided. In developing a surface reaction mechanism, one may choose to specify independently the forward and reverse rate constants for each reaction. An alternative would be to specify the change in free energy (as a function of temperature) for each reaction, and compute the reverse rate constant via the reaction equilibrium constant. 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

The equilibrium constants for heterogeneous reactions are given by the general expression in Eq. 8a all we have to remember is that the... 

A useful empirical approach to the design of heterogeneous chemical reactors often consists of selecting a suitable equation, such as one in Table 3.3 which, with numerical values substituted for the kinetic and equilibrium constants, represents the chemical reaction in the absence of mass transfer effects. Graphical methods are often employed to aid the selection of an appropriate equation140 and the constants determined by a least squares approach<40). It is important to stress, however, that while the equation selected may well represent the experimental data, it does not... 

The condition of equilibrium is also applicable to changes of state that involve heterogenous reactions, and the same methods used for homogenous reactions to obtain expressions of the equilibrium constant are used for heterogenous reactions. One difference is that in many heterogenous reactions one or more of the substances taking part in the change of state is a pure phase at equilibrium. In such cases the standard state of the substance is chosen as the pure phase at the experimental temperature and pressure. The chemical potential of the pure substance in its standard state still appears in Y.k vkPk but the activity of the substance is unity and its activity does not appear in the expression for the equilibrium constant. 

An equilibrium constant for the heterogeneous reaction in equation (9.2) can be defined in terms of activities (denoted by bold parentheses) ... 

The apparent rate constant in (2.10), which is obtained by multiplying a true rate constant kc and the square root of an equilibrium constant, Keq, can show a law of dependence on temperature different from the simple Arrhenius law. In some cases, even a negative temperature dependence can be observed. Moreover, if both mechanisms (2.6) and (2.7)-(2.8) are active in parallel, the observed reaction rate is the sum of the single rates, and an effective reaction order variable from 1 /2 to 1 can be observed with respect to reactant A. Variable and fractionary reaction orders can be also encountered in heterogeneous catalytic reactions as a consequence of the adsorption on a solid surface [6],... 

Electrochemical methods are well established and use relatively inexpensive equipment to produce unique characterization information for molecules and chemical systems qualitative (speciation) and quantitative analytical data, thermodynamic data (equilibrium constants), and kinetic data (heterogeneous and homogeneous reaction rates). 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

In soil solutions the most important chemical elements that undergo redox reactions are C, N, O, S, Mn, and Fe. For contaminated soils the elements As, Se, Cr, Hg, and Pb could be added. Table 2.4 lists reduction half-reactions (most of which are heterogeneous) and their equilibrium constants at 298.15 K under 1 atm pressure for the six principal elements involved in soil redox phenomena. Although the reactions listed in the table are not full redox reactions, their equilibrium constants have thermodynamic significance and may he calculated with the help of Standard-State chemical potentials in the manner... 

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